FIN 301 - Ch.3 TWM Prof. Choi

What is the present value of $500 to be received in 5 years? The discount rate is 10%

PV = 500(1.1)^-5 = 310.46

What is the present value of $500 to be received in 5 years? The discount rate is 15%

PV = 500(1.15)^-5 = 248.58

What is the present value general formula?

PV0 = FVt ( 1 + r/m )^ -(m)(t)

Suppose you invest $1000 at an annual interest rate of 12% compounded quarterly for 5 years. How much would you have? Use both compounding and simple method.

Compounding: 1000 (1+0.12/4)^(4)(5) = 1000 (1.8061)^(20) = 1,806.1112 Simple: 1000(0.12/4) = 30 x 4 = 120 x 5 = 600

What does the following stand for: 1) m = 1: compound ___________ 2) m = 2: compound ____________ 3) m = 4: compound _____________ 4) m = 365: compound _____________

1) annually 2) semi-annually 3) quarterly 4) daily

72 Rule: Suppose you have a deposit of $100 and it pays 10% interest per year. How long it will take to double your deposit balance?

72/10yrs = 7.2 years

Suppose you borrow $10,000 from your parents to buy a car. You agree to pay $207.58 per month at the end of each month for 60 months. What is your monthly interest rate?

N = 60 Pv = 10000 PMT = -207.58 FV = 0 I/Y = -----> 0.7499 monthly x 12 = 9

You are saving for a new house and you put $10,000 per year in an account paying 8%. The first payment is made today. How much will you have at the end of 3 years?

BGN N = 3 I = 8 PMT = 10,000 PV = 0 FV = ----> 25,061.12

Invest $100, get $40 in your 1st year and $75 on your 2nd year. What is the IRR?

CFO = -100 CO1 = 40 CO2 = 75 IRR = 8.8819

You are offered the opportunity to put your money away for retirement. You will receive five annual payments of $25,000 each beginning in 40 years. How much would you be willing to invest today if you desire an interest rate of 12% per year?

CFO = 0 CO1 = 0 FO1 = 39 CO2 = 25,000 FO2 = 5 I = 12 NPV = 1084.71

You are considering an investment that will pay you $1000 in one year, $2000 in two years and $3000 in three years. If you want to earn 10% per year on your money, how much would you be willing to pay?

CFO = 0 CO1 = 1,000 CO2 = 2,000 CO3 = 3,000 I = 10 NPV = 4815.93

Your broker calls you and tells you that he has this great investment opportunity. If you invest $100 today, you will receive $40 in one year and $75 in two years. If you require a 15% return per year on investments of this risk, should you take the investment?

CFO = 0 CO1 = 40 CO2 = 75 I = 15 NPV = 91.49 No, because its less than $100

Suppose you invest $1000 at an annual interest rate of 12% compounded quarterly. What is the compounded interest over one year? What is the simple interest over 1 year?

Compounded interest: n = 1 x 4 = 4 i = 12/4 = 3 PV = 1000 ------> FV = 1,125.51 - 1,000 = 125.51 Simple interest: 1000 x (1 + 0.12) = 120

Suppose you had a deposit $10 at quarterly compounding annual interest rate of 5.5% 200 years ago. How much would the investment be worth today? With both compounding and simple method:

Compounding: n = 200 x 4 = 800 i = 5.5/4 = 1.3750 PV = -10 ------> FV = 555,512.4227 Simple: 10(0.055) = 0.55 x 200 = 110 Difference: 110+10 = 120 - 555,512 = 555,392

Suppose you invest $500 in a mutual fund today and $600 in one year. If the fund pays 9% annually, how much will you have in two years?

FV = 500(1.09)^2 + 600(1.09) = 1248.05

What is the future value general formula?

FVt = PV0 ( 1 + r/m )^ (m)(t)

Suppose you begin saving for your retirement by depositing $2000 per year in an IRA at the end of each year. If the interest rate is 7.5%, how much will you have in 40 years?

N = 40 I = 7.5 PV = 0 PMT = 2000 FV = ----> 454,513.0392

Suppose you want to borrow $20,000 for a new car. You can borrow at 8% per year, compounded monthly (8/12 = 0.66667% per month). If you take 4 year loan, what is your monthly payment?

N = 48 i = 0.0066667 PV = 20,000 FV = 0 PMT = -----> 417.3476

Suppose you plan to deposit $100 into an account in one year and $300 into the account in three years. How much will be in the account in five years if the interest rate is 8%

Year 0: 0 Year 1: $100(1.08)^4 = 136.0489 Year 2: 0 Year 3: 300(1.08)^2 = 349.92 Year 4: 0 NPV = 485.920

You are expected to receive $200 at the end of first year, $400 the 2nd year, $600 the 3rd year and $800 the 4th year. If the appropriate interest rate is 12% per year, how much is the total value worth today?

Year 0: 0 Year 1: $200/(1.12)^1 = 178.5714 Year 2: $400/(1.12)^2 = 318.8776 Year 3: $600(1.12)^3 = 427.0767 Year 4: $800/(1.12)^4= 508.41 = 14322.23 or CF0 = 0 CO1 = 200 CO2 = 400 CO3 = 600 CO4 = 800 I = 12 NPV = 1,432.9316

Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?

n = 1 i = 7 PMT = 0 FV = 10,000 -----> PV = 9345.79

Deposit $100 in a savings account that pays an interest of 10% per year. What would be the balance at the end of the 1st year? What is the future value of the $100 at the end of 1 year?

n = 1 PV = 100 i = 10 pmt = 0 -----> FV = 110

Your parents set up a trust fund for you 10 years ago that is now worth $19,671.51. If the fund earned 7% per year, how much did your parents invest?

n = 10 i = 7 PV = ----> 9999.9982 or 10,000 PMT = 0 FV = 19.671.51

Suppose you have a 1-year old son and you want to provide $75,000 in 17 years toward his college education. You currently have $5,000 yo invest. What interest rate must you earn to have the $75,000 when you need it?

n = 17 PV = -5000 PMT = 0 FV = 75,000 I = -----> 17.2686

You want to begin saving for your daughter's college education and you estimate that she will need $150,000 in 17 years. If you feel confident that you can earn 8% per year, how much do you need to invest today?

n = 17 i = 8 PMT = 0 FV = 150,000 -----> PV = 40,540.3427

Deposit $100 in a savings account that pays an interest of 10% per year. What is the future value of the $100 at the end of 2nd year?

n = 2 PV = 100 i = 10 pmt = 0 -----> FV = 121

Suppose you need $15,000 in 3 years. If you can earn 6% annually, how much do you need to invest today?

n = 3 i = 6 PMT = 0 FV = 15,000 PV = ------> 12,594.2892

You think you will be able to deposit $4,000 at the end of each year for the next three years in a bank account paying 8% of annual interest rate compounded annually. You currently have $7,000 in the account. How much will you have in three years?

n = 3 i = 8 PV = 7,000 PMT = 4,000 FV = -----> 21,803.5840

Suppose you win the Publishers Clearinghouse $10 million sweepstakes. The money is paid in equal annual installations of $333,333.33 at the end of each year over 30 years. If the appropriate discount rate is 5% per year, how much are the sweepstakes actually worth today?

n = 30 i = 5 PMT = 333,333.33 FV = 0 PV = ----> 5,124,150.291

Discount Rate: You are looking at an investment that will pay $1200 in 5 years if you invest $1000 today. What is the implied Annual rate of interest compounded annually?

n = 5 PV = -1000 FV = 1200 PMT = 0 I = ----> 3.714%

Discount Rate: Suppose you are offered an investment that will allow you to double your money in 6 years. You have $10,000 to invest. What is the implied annual rate of interest compounded semi-annually.

n = 6 x 2 = 12 PV = -10,000 PMT = 0 FV = 20,000 I = -----> 5.9463 x 2 = 11.8926